Find the limit where , where [ ] indicates the Floor Function.. The given limits are
Note the following important points:
The Sandwich theorem also known as squeeze play theorem applicable for any three real valued functions and that shares the same domain such that for
in the domain of definition states the following:
The Floor Function indicates the greatest integer function [GIF] denoted mathematically as for only real values. This function rounds downs the real number having any fractional or decimal part (if any) to the nearest integral value less than the indicated number.
From the definition of GIF, the following is evident.
--------(i)
The provided limits are
Now, multiply the inequality (i) by the reciprocal of
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